[Forum SIS] Seminario Rajen Shah

[Aldo Solari]

Buongiorno,



Mercoledì 4 Novembre, ore 13


Rajen Shah <http://www.statslab.cam.ac.uk/~rds37/>, dell'Università di
Cambridge,


terrà un seminario (da remoto) dal titolo:


*Low-priced lunch in conditional independence testing*.


Per accedere al seminario usare questo collegamento
<https://unimib.webex.com/unimib/onstage/g.php?MTID=ee62fd9c000f8d4e30a3b2053f6cdac2a>
 .


(Per chi si collega da *smartphone* specificare *event password*: 04112020)


Sintesi


*It is a common saying that testing for conditional independence, i.e.,
testing whether X is independent of Y, given Z, is a hard statistical
problem if Z is a continuous random variable. We provide a formalisation of
this result and show that any test must have size at least as large as its
power - in this sense conditional independence testing is impossible! In
the case where Z is infinite-dimensional (e.g. if Z is a functional
predictor), the problem is more severe: even if (X, Y, Z) are assumed to be
jointly Gaussian, and the marginal distribution of Z is known, testing
conditional independence is impossible.*


*Given the non-existence of uniformly valid conditional independence tests,
we argue that tests must be designed so their suitability for a particular
problem setting may be judged easily. To address this need, we propose a
simple family of conditional independence tests valid for both the
multivariate and functional data settings whose validity relies primarily
on the relatively weak requirement that regressing each of X and Y on Z is
able to estimate the relevant conditional expectations at a slow rate.
While our general procedure can be tailored to the setting at hand by
combining it with any regression technique, we develop theoretical
guarantees for kernel ridge regression and Tikhonov regularisation in the
context of the functional linear model. Simulation studies show that our
testing framework is competitive with state of the art conditional
independence tests.*



Questo webinar è il primo della serie *DEMS Statistics Webinar* organizzati
dal Prof. Bernardo Nipoti dell’Università di Milano-Bicocca. I prossimi
seminari:


18 Novembre 2020 ore 13 : François Caron, Università di Oxford

25 Novembre 2020 ore 17 : Andrés Felipe Barrientos, Università statale
della Florida

2 Dicembre 2020 ore 17: Matteo Sesia, Università della California del sud


Un cordiale saluto
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